Gunfire characterization and simulation using temporal moments

The concept of band-limited temporal moments is briefly reviewed. An input-output relationship for the band-limited product model is derived. The band-limited product model is then used to characterize and simulate a gunfire record in the following manner. An ensemble of 50 gunfire rounds are averaged to determine the mean response. The mean is subtracted from the original record and the remaining signal is characterized using a smoothed mean square response of the signal filtered into contiguous bandwidths. This operation preserves the lower bandlimited temporal moments of the original data. This smoothed mean square response was used as the deterministic window for the product model. The power spectrum of the response with the mean removed is used to estimate the spectrum for the random part a product model. An additional step varied the repetition rate in a random manner of the simulated gunfire rounds to match the original record in a statistical sense.